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A260002 Sudan Numbers: a(n)= f(n,n,n) where f is the Sudan function. 5
0, 3, 15569256417 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Sudan function is the first discovered not primitive recursive function that is still totally recursive like the well-known three-argument (or two-argument) Ackermann function ack(a,b,c) (or ack(a,b)).

The Sudan function is defined as follows:

f(0,x,y) = x+y;

f(z,x,0) = x;

f(z,x,y) = f(z-1, f(z,x,y-1), f(z,x,y-1)+y).

Just as the three-argument (or two-argument) Ackermann numbers A189896 (or A046859) are defined to be the numbers that are the answer of ack(n,n,n) (or ack(n,n)) for some natural number n, the Sudan numbers are: a(n) = f(n,n,n).

a(3)> 2^(76*2^(76*2^(76*2^(76*2^76)))) so is too big to be included.

LINKS

Table of n, a(n) for n=0..2.

Wikipedia, Sudan Function, Primitive Recursive, Ackermann function.

EXAMPLE

a(1) = f(1,1,1) = f(0, f(1,1,0), f(1,1,0)+1) = f(0, 1, 2) = 1+2 = 3.

MATHEMATICA

f[z_, x_, y_] := f[z, x, y] =

Piecewise[{{x + y, z == 0}, {x,

    z > 0 && y == 0}, {f[z - 1, f[z, x, y - 1], f[z, x, y - 1] + y],

    z > 0 && y > 0} }];

a[n_] := f[n, n, n]

PROG

(PARI) f(z, x, y)=if(z, if(y, my(t=f(z, x, y-1)); f(z-1, t, t+y), x), x+y)

a(n)=f(n, n, n) \\ Charles R Greathouse IV, Jul 28 2015

CROSSREFS

Cf. A189896, A046859, A260003, A260004, A260005, A260006.

Sequence in context: A154998 A036236 A235357 * A058447 A275939 A230810

Adjacent sequences:  A259999 A260000 A260001 * A260003 A260004 A260005

KEYWORD

nonn,bref,changed

AUTHOR

Natan Arie' Consigli, Jul 12 2015

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)